Up to now, a method of decomposing the original image signal F into a skeleton component (geometrical image structure) and a component other than the skeleton component and extracting the components, is disclosed in the following document: Jean-Francois Aujol, Guy Gilboa, Tony Chan & Stanley Osher, “Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection”, International Journal of Computer Vision, Volume 67, Issue 1, (April 2006) Pages: 111-136, Year of Publication: 2006. The skeleton component is a component representing a global structure, and includes a flat component (component that varies gently) and an edge component. The component other than the skeleton component is a component representing a local structure, and includes a detailed structural component such as a texture, and a noise.
As a method of decomposing an image, there are addition type separation and multiplication type separation. In the addition type separation, the original image signal F is expressed as the sum of a first component U and a second component V as illustrated in Equation (1).F=U+V  (1)
The first component U is a skeleton component. The second component V other than the skeleton component includes a texture component and a noise, and is defined as a remainder component obtained by subtracting the first component U from the original image signal F.
Herein, a decomposition method employing a bounded variation function and a norm is used. An Aujol-Aubert-Blanc-Feraud-Chambolle model (A2BC variation model) described in “Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection” is used for decomposition. A property of the first component U determined as an optimal solution is modeled as a bounded variation function space (BV) constituted by a plurality of “smooth luminance variation small part regions” compartmentalized by discrete boundaries. The energy of the first component U is defined as a total variation energy by a total-variation (TV) norm J(U) illustrated in Equation (2).J(U)−∫∥ΛU∥dxdy  (2)In Equation (2), x represents a pixel position in a horizontal direction of the first component U, and y represents a pixel position in a vertical direction thereof.
Meanwhile, a function space of the second component V in Equation (1) is modeled as an oscillation function space G. The oscillation function space G is a function space expressed by oscillation generating functions g1 and g2 as illustrated in Equation (3), and the energy thereof is defined as G norm ∥V∥G in Equation (4).
                                                        V                              (                                  x                  ,                  y                                )                                      =                                                            ∂                  x                                ⁢                                  g                                      l                    ⁡                                          (                                              x                        ,                        y                                            )                                                                                  +                                                ∂                  x                                ⁢                                  g                                      2                    ⁢                                          (                                              x                        ,                        y                                            )                                                                                                    ;                      g            1                          ,                              g            2                    ∈                                    L              ∞                        ⁡                          (                              R                2                            )                                                          (        3        )                                                                  V                                G                =                              inf                                          g                ⁢                                                                  ⁢                1                            ,                              g                ⁢                                                                  ⁢                2                                              ⁢                      {                                                                                                                                                (                                                  g                          1                                                )                                            2                                        +                                                                  (                                                  g                          2                                                )                                            2                                                                                                          L                  ⁢                                                                          ⁢                  ∞                                            ;                              V                =                                                                            ∂                      x                                        ⁢                                          g                      1                                                        +                                                            ∂                      x                                        ⁢                                          g                      2                                                                                            }                                              (        4        )            
A decomposition problem of the original image signal F is formulated as a variation problem of Equation (5) for minimizing an energy functional. The variation problem can be solved by the projection method of Chambolle.
                                          inf                          U              ,                              V                ∈                                  G                  μ                                                              ⁢                      {                                          J                ⁡                                  (                  U                  )                                            +                                                1                                      2                    ⁢                    α                                                  ⁢                                                                                                F                      -                      U                      -                      V                                                                                                L                    2                                    2                                                      }                          ⁢                                  ⁢                              α            >            0                    ,                      μ            >            0                    ,                                    G              μ                        =                          {                                                V                  ∈                  G                                |                                                                                                  V                                                              G                                    ≤                  μ                                            }                                                          (        5        )            
The second component V separated from the original image signal F receives a noise effect. However, the first component U receives substantially no noise effect, and hence the skeleton component (geometrical image structure) is extracted without blunting an edge.
In the multiplication type separation, the original image signal F is expressed by the product of the first component U and the second component V as illustrated in Equation (6). However, when a logarithmic original image signal obtained by logarithmically transforming the original image signal F is set as f, the multiplication type separation can be transformed into an addition type separation problem as illustrated in Equation (7).F=U*V  (6)f=u+v (f=log F, u=log U, v=log V)  (7)